Airfoil mateface sealing

ABSTRACT

An airfoil includes an airfoil working portion and an adjoining endwall. The endwall has a leading edge, a trailing edge, a first mateface, and a second mateface that collectively define a perimeter of the endwall, with the first and second matefaces arranged opposite one another. A forward zone is defined by the endwall that extends to the leading edge. The first and second matefaces are each oriented at an angle α II  relative to radial in the forward zone. An aft zone is defined by the endwall that extends to the trailing edge. The first and second matefaces are each oriented at an angle α II  relative to radial in the aft zone. The angles α II  and α II  are not equal. A middle zone is defined in between the forward and aft zones, and the first and second matefaces transition between the angles α II  and α I  in the middle zone.

BACKGROUND

The present invention relates to airfoil mateface sealing, and moreparticularly to an apparatus and associated method for sealing adjoiningmatefaces of airfoil platforms.

In gas turbine engines, cascades of airfoils are provided in a primarygas flowpath. These airfoil cascades can include rotatable blades and/ornon-rotating stator vanes. Typical blades and stators include an airfoiladjoining a platform at its root or hub end, and possibly also at ashroud at an opposite tip end. Collectively platforms and shrouds can bereferred to as endwalls, which define boundaries of the primary gasflowpath. In modern engines these endwalls are often segmented, suchthat an endwall segment is integrally formed or attached to eachairfoil. Adjacent endwall segments in the cascade adjoin each other atmatefaces. Matefaces are generally separated by small gaps. In hot(e.g., turbine) sections of a gas turbine engine, airfoil cascades maybe cooled with a cooling fluid, a portion of which may flow through thegaps between endwall matefaces and into the primary flowpath.

In a basic prior art design, as shown in FIGS. 2A and 3A, endwallmatefaces are machined radially with a break edge. Various endwall orplatform designs are known to reduce vortices produced in fluid passingthrough the primary flowpath and other aerodynamic losses, such as thatshown in FIG. 3B.

However, it is desired to provide improved endwall matefaces thatfurther reduce vortices and secondary losses (i.e., pressure losses) inthe primary flowpath.

SUMMARY

An airfoil for use in an airfoil cascade according to the presentinvention includes an airfoil working portion and an adjoining endwall.The endwall has a leading edge, a trailing edge, a first mateface, and asecond mateface that collectively define a perimeter of the endwall,with the first and second matefaces arranged opposite one another. Aforward zone is defined by the endwall that extends to the leading edge.The first and second matefaces are each oriented at an angle α_(II)relative to radial in the forward zone. An aft zone is defined by theendwall that extends to the trailing edge. The first and secondmatefaces are each oriented at an angle α_(I) relative to radial in theaft zone. The angles α_(I) and α_(II) are not equal. A middle zone isdefined in between the forward and aft zones, and the first and secondmatefaces transition between the angles α_(II) and α_(I) in the middlezone.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of a pair of adjacent airfoils having adjoiningendwall matefaces.

FIG. 2A is a cross-sectional view of a prior art endwall matefaceconfiguration.

FIGS. 2B and 2C are cross-sectional views of embodiments of endwallmateface configurations according to the present invention.

FIGS. 3A and 3B are cross-sectional views of prior art endwall matefaceconfigurations and associated airflow patterns.

FIGS. 3C and 3D are cross-sectional views of the endwall matefaceconfiguration of FIGS. 2B and 2C, respectively, and associated airflowpatterns.

FIGS. 4A-4D are cross-sectional views of various embodiments of endwallmateface configurations according to the present invention.

FIGS. 5A-5D are cross-sectional views of the various embodiments ofendwall mateface configurations of FIGS. 4A-4D, taken at different axiallocations than the views shown in FIGS. 4A-4D.

While the above-identified drawing figures set forth embodiments of theinvention, other embodiments are also contemplated, as noted in thediscussion. In all cases, this disclosure presents the invention by wayof representation and not limitation. It should be understood thatnumerous other modifications and embodiments can be devised by thoseskilled in the art, which fall within the scope and spirit of theprinciples of the invention. The figures may not be drawn to scale, andapplications and embodiments of the present invention may includefeatures and components not specifically shown in the drawings.

DETAILED DESCRIPTION

FIG. 1 is a top view of a pair of adjacent airfoils 20A and 20B(generically referred to as simply airfoils 20) each having an airfoilworking portion 22 and an endwall 24. The airfoils 20A and 20B can beused in a gas turbine engine (not shown), and can form part of a cascadeof similarly-configured airfoils. The working portions 22 each have apressure side 22P and an opposite suction side 22S defined between aleading edge 22LE and a trailing edge 22TE. In the illustratedembodiment, the airfoil working portion 22 is cambered. The endwalls 24each have matefaces 26 and 28 along opposing lateral edges, as well as aleading edge 30 and trailing edge 32. The matefaces 26 and 28 and theedges 30 and 32 collectively define a perimeter of each endwall 24. Theendwall mateface 26 of the airfoil 20A adjoins the mateface 28 of theairfoil 20B, with a small gap 34 between the adjoining matefaces 26 and28 of the respective airfoils 20A and 20B. A size of gap 34 can vary forparticular applications and can potentially vary during use, such asduring different operational conditions. A flowpath surface 36 isdefined by the endwalls 24 adjacent to each of the matefaces 26 and 28and the edges 30 and 32 that extends to the perimeter collectivelydefined by the matefaces 26 and 28 and the edges 30 and 32, such thatthe perimeter of the endwalls 24 is also the perimeter of the flowpathsurface 36. The flowpath surface 36 can have nearly any desiredconfiguration, such as an axisymmetric or non-axisymmetric contour.Sealing between the adjacent airfoils 20A and 20B is defined at least inpart by the matefaces 26 and 28 and the gap 34.

The airfoils 20A and 20B can be positioned in a primary flowpath of agas turbine engine, with the endwalls 24 defining segments or portionsof a boundary of the primary flowpath. In the illustrated embodiment theairfoils 20A and 20B are represented as rotatable turbine blades, but infurther embodiments the airfoils 20A and 20B can be turbine statorvanes, or could alternatively be blades or vanes of a compressor sectionof the engine. The endwalls 24 can be configured as platforms located ator adjoining a root or hub end of the working portions 22 or as shroudslocated at or adjoining a tip end of the working portions 22, and theendwalls 24 can be integrally and monolithically formed with the workingportions 22, in various embodiments. The basic configuration of gasturbine engines is well known in the art, and therefore furtherexplanation here is unnecessary. The configuration of the workingportions 22 and other features of the airfoils 20A and 20B are shownmerely by way of example, and not limitation. Those of ordinary skill inthe art will recognize that a variety of airfoil configurations arepossible for use in conjunction with the present invention.

FIG. 2A is a cross-sectional view of a prior art endwall matefaceconfiguration taken along line I-I of FIG. 1, with the matefaces 26 and28 both radially oriented along an entire distance from the leading edge30 to the trailing edge 32 of the endwall 24. The matefaces 26 and 28each form right angles at respective intersections with the flowpathsurfaces 36.

FIGS. 2B and 2C are cross-sectional views of embodiments ofconfigurations of the endwall matefaces 26 and 28, taken along lineII-II of FIG. 1 (for simplicity, structures beyond the section plane arenot shown in FIGS. 2B and 2C).

In the embodiment illustrated in FIG. 2B, an arcuate flow modifying edge38 is formed at a boundary between the mateface 26 and the flowpathsurface 36, and an arcuate flow modifying edge 40 is formed at aboundary between the mateface 28 and the flowpath surface 36. The flowmodifying edges 38 and 40 can each extend along the entire lengths ofthe matefaces 26 and 28 between the leading edge 30 and the trailingedge 32 of the endwalls 24 (see also FIG. 3C). Each flow modifying edge38 and 40 can be generally arcuate with a radius R. In one embodiment,the radius R is approximately 0.127 to 6.35 mm (0.005 to 0.250 inch), oranother range significantly or substantially larger than a break edgeradius. In another embodiment, the radius R can be established as afunction of a size of the gap 34, measured as circumferential distanceG, such as with the relationship 0.5×G≦R≦2×G. In the illustratedembodiment, the flow modifying edges 38 and 40 have a substantiallyidentical configuration (i.e., identical radius R), though inalternative embodiments the configurations of the flow modifying edges38 and 40 can be different from one another (e.g., having differentradiuses R). In still further embodiments, the flow modifying edges 38and 40 can be defined by other types of curved surfaces (e.g.,elliptical, parabolic, complex polynomial, etc.), rather than a simpleradius.

In the embodiment illustrated in FIG. 2C, a chamfered flow modifyingedge 42 is formed at a boundary between the mateface 26 and the flowpathsurface 36, and a chamfered flow modifying edge 44 is formed at aboundary between the mateface 28 and the flowpath surface 36. The flowmodifying edges 42 and 44 can each extend along the entire lengths ofthe matefaces 26 and 28 between the leading edge 30 and the trailingedge 32 of the endwalls 24. Each chamfered edge 42 and 44 can beoriented at an angle θ with respect to the respective adjoiningmatefaces 26 and 28. In one embodiment, the angle θ is approximately 45°to 75°. In another embodiment, the angle θ can be established as afunction of a size of the gap 34, measured as the circumferentialdistance G, such as θ=a×tan (o/a), where a is a radial dimension of thechamfered edges 42 and 44 and o is a circumferential dimension of thechamfered edges 42 and 44. In one embodiment, the relationships0.5×G≦o≦2×G and 0.5×G≦a≦2×G can be established. Further, o can begenerally greater than a.

By having the flow modifying edges 38, 40, 42 and 44 extend along entirelengths of the corresponding matefaces 26 and 28, from the leading edge30 to the trailing edge 32, manufacturing can be simplified as comparedto flow modifying structures that extend only partially along themateface 26 or 28. Flow modifying benefits are also obtained by havingthe flow modifying edges 38, 40, 42 and 44 extend along entire lengthsof the corresponding matefaces 26 and 28, from the leading edge 30 tothe trailing edge 32.

In further embodiments, different flow modifying edge configurations canbe utilized for different edges of a single endwall 24. For instance, achamfered flow modifying edge 42 can be used adjacent to the mateface 26and an arcuate flow modifying edge 40 can be used adjacent to themateface 28 for a given endwall 24, or vice-versa.

Although not shown in FIGS. 2B and 2C, it should be understood thatadditional features can be included with the illustrated endwalls 24 infurther embodiments. For example, feather seals, ladder seals or othersealing structures can be used to help seal the gap 34, and dampingstructures can be positioned at or near the endwalls 24. Additionally,cooling holes can be provided in the platforms 24, such as in any of thematefaces 26 and/or 28, and/or in any of the flow modifying edges 38,40, 42 and/or 44.

FIGS. 3A and 3B are cross-sectional views of prior art endwall matefaceconfigurations and associated airflow patterns, taken along line II-IIof FIG. 1. FIG. 3A illustrates airflow for the configuration shown inFIG. 2A. As shown in FIG. 3A, relatively large vortices 50 and 50′ areformed as the fluid flow 52 of the primary flowpath passes the gap 34.The vortices 50 and 50′ produce secondary losses, specifically pressureloses, that undesirably reduce efficiency. FIG. 3B illustrates anotherprior art endwall configuration, which has a rounded edge 54 at themateface 26 that is downstream relative to the fluid flow 52 but a rightangle edge along the upstream mateface 28. The rounded edge 54 extendsalong only a portion of the mateface 26, and does not extend an entirelength between a leading edge 30 and trailing edge 32 of the endwall 24.As the fluid flow 52 passes the gap 34, relatively large vortices 50 arestill formed in the gap 34, though a reduction or elimination of thevortices 50′ has been achieved.

FIGS. 3C and 3D are a cross-sectional views of endwall matefaceembodiments of FIGS. 2B and 2C, respectively, and associated airflowpatterns. The cross-sections of FIGS. 3C and 3D are taken along lineII-II of FIG. 1. As shown in FIG. 3C, a size and magnitude of vortices50 at the gap can be achieved in comparison to the prior artconfigurations shown in FIGS. 3A and 3B, reducing in reduced secondarypressure and mixing losses and produce less turbulent flow that exhibitsrelatively little flow separation. The airflow 32 closely follows orhugs the endwall 24 as a result of both the upstream flow modifying edge40 or 44 and the downstream flow modifying edge 38 or 42. In addition,as shown in FIGS. 3C and 3D, the vortices 50′ can be reduced oreliminated as compared to FIG. 3A. It should be noted that reference to“upstream” and downstream” refer to the illustrated embodiment, as bestshown in FIG. 1, in which the fluid flow 52 of the primary flowpathapproaches the gap 34 at a generally transverse angle at or near thesection line II-II. Particular flow characteristics will vary forparticular applications, based on the configurations of the airfoils 20Aand 20B and fluid flow characteristics upstream from the airfoils 20Aand 20B.

In further embodiments, an interface of the matefaces 26 and 28 ofadjacent endwalls 24 at the gap 34 can have different angularorientations relative to the radial direction, as shown in theembodiments illustrated in FIGS. 4A-5D. More specifically, the matefaces26 and 28 can each be oriented at an angle α relative to the radialdirection (see FIGS. 4B and 5B). The angle α can be the same for bothadjoining matefaces 26 and 28 in one embodiment, such that the adjoiningmatefaces 26 and 28 can be parallel. The angle α can be constant alongthe matefaces 26 and 28 from the leading edge 30 to the trailing edge 32of the endwalls 24. Alternatively, the angle α can vary along a lengthof the matefaces 26 and 28 between the leading edge 30 and the trailingedge 32. Variation in the angle α can be implemented in zones. Forexample, a forward zone 100 that extends to the leading edge 30, an aftzone 102 that extends to the trailing edge 32, and a middle zone 104located between the forward and aft zones 100 and 102 can be defined. Inthe forward zone 100 the angle α can be constant at a value α_(II), inthe aft zone 102 the angle α can be constant at a value a₁, and in themiddle zone 104 a transition in the angle α can be made between theangles α_(I) and α_(II), that is, the angle α can vary between theangles α_(I) and α_(II) such that a relatively smooth transition inprovided at boundaries between the middle zone 104 and each of theforward and aft zones 100 and 102.

In some embodiments, at least portions of the matefaces 26 and 28 can besubstantially planar. For example, the forward zones 100 and aft zones102 of the matefaces 26 and 28 can be substantially planar, while themiddle zone 104 would generally be non-planar to accomplish thevariation in the angle α. In alternatively embodiment, curved ornon-linear endwalls 24 can be used, such that the matefaces 26 and 28have significant non-planar regions.

FIGS. 4A-4D are cross-sectional views of various additional embodimentsof endwall mateface configurations taken along line I-I of FIG. 1. Asshown in the embodiment illustrated in FIG. 4A, the angle α of thematefaces 26 and 28 is 0° and no flow modifying edge is present betweenthe matefaces 26 and 28 and the flowpath surface 36 of the endwalls 24.A secondary flow 152 is shown passing through the gap 34 toward a fluidflow 52′ of the primary flowpath. Here is should be noted that asillustrated in FIG. 1, the fluid flow 52 that enters a throat areabetween the adjacent airfoils 20A and 20B changes direction (i.e.,turns) relative to an axial direction to form the exiting fluid flow52′. The secondary flow 152 can be a cooling air flow that mixes withthe fluid flow 52 and 52′ of the primary flowpath. As shown in theembodiment illustrated in FIG. 4B, the matefaces 26 and 28 are arrangedat a non-zero angle α relative to the radial direction (where the angleα is positive in a clockwise direction when looking forward, that is, tothe right in FIGS. 4A-4D), such that the secondary flow 152 is at leastpartially angled from the radial direction in generally the samedirection as the fluid flow 52′. No flow modifying edge is presentbetween the matefaces 26 and 28 and the flowpath surface 36 of theendwalls 24 as shown in FIG. 4B. As shown in FIG. 4C, arcuate flowmodifying edges 38 and 40 are present between the matefaces 26 and 28and the flowpath surface 36 of the endwalls 24, and the matefaces 26 and28 are arranged at a non-zero angle α relative to the radial direction,such that the secondary flow 152 is at least partially angled from theradial direction in generally the same direction as the fluid flow 52′.As shown in FIG. 4D, chamfered flow modifying edges 42 and 44 arepresent between the matefaces 26 and 28 and the flowpath surface 36 ofthe endwalls 24, and the matefaces 26 and 28 are arranged at a non-zeroangle α relative to the radial direction, such that the secondary flow152 is at least partially angled from the radial direction in generallythe same direction as the fluid flow 52′.

FIGS. 5A-5D are cross-sectional views of the various embodiments ofendwall mateface configurations, taken along line II-II of FIG. 1. Asshown in the embodiment illustrated in FIG. 5A, the angle α of thematefaces 26 and 28 is 0° and no flow modifying edge is present betweenthe matefaces 26 and 28 and the flowpath surface 36 of the endwalls 24.A secondary flow 152 is shown passing through the gap 34 toward a fluidflow 52′ of the primary flowpath. As shown in the embodiment illustratedin FIG. 5B, the matefaces 26 and 28 are arranged at a non-zero angle αrelative to the radial direction, such that the secondary flow 152 is atleast partially angled from the radial direction in generally the samedirection as the fluid flow 52. No flow modifying edge is presentbetween the matefaces 26 and 28 and the flowpath surface 36 of theendwalls 24 as shown in FIG. 5B. As shown in FIG. 5C, arcuate flowmodifying edges 38 and 40 are present between the matefaces 26 and 28and the flowpath surface 36 of the endwalls 24, and the matefaces 26 and28 are arranged at a non-zero angle α relative to the radial direction,such that the secondary flow 152 is at least partially angled from theradial direction in generally the same direction as the fluid flow 52.As shown in FIG. 5D, chamfered flow modifying edges 42 and 44 arepresent between the matefaces 26 and 28 and the flowpath surface 36 ofthe endwalls 24, and the matefaces 26 and 28 are arranged at a non-zeroangle α relative to the radial direction, such that the secondary flow152 is at least partially angled from the radial direction in generallythe same direction as the fluid flow 52.

In one embodiment, an absolute value of the angle α can be in the rangeof approximately 0°≦|α|≦45°. In a further embodiment, the angle α₁ inthe forward zone 100 can be in the range of approximately 0°<α_(II)≦45°,and the angle α₂ in the aft zone 102 can be in the range ofapproximately −45°≦α_(I)≦0° (where α_(I)≠α_(II)). In still a furtherembodiment, the angle α_(II) in the forward zone 100 can be in the rangeof approximately −45°≦α_(II)≦0°, and the angle α_(I) in the aft zone 102can be in the range of approximately 0°<α_(I)<45° (where α_(I)≠α_(II)).In one embodiment, the angle α_(II) in the forward zone 100 can beapproximately 0° and the angle α_(I) in the aft zone 102 can be in therange of approximately 0°<α_(I)≦45°. In an alternative embodiment, theangle α_(II) in the forward zone 100 can be in the range ofapproximately −45°≦α_(II)<0° and the angle α_(I) in the aft zone 102 canbe approximately 0°. It is possible to incorporate the flow modifyingedges 38, 40, 42 and/or 44 into embodiments of the endwalls 24 havingany angle or angles α.

It may be desirable for simplification of assembly of the airfoils 20Aand 20B into a corresponding mounting structure, such as a rotor disk orcase (not shown) having one or more airfoil retention slots of aconventional configuration, to have the angle α of the matefaces 26 and28 in the forward or aft zone 100 or 102 to be 0° or close to 0°. Forexample, in one embodiment, the matefaces 26 and 28 can have the angle αbe zero or near-zero in the forward zone 100. In an alternativeembodiment, the matefaces 26 and 28 can have the angle α be zero ornear-zero in the aft zone 102.

Although not shown in FIGS. 4A-5D, it should be understood thatadditional features can be included with the illustrated endwalls 24 infurther embodiments. For example, feather seals, ladder seals or othersealing structures can be used to help seal the gap 34, and dampingstructures can be positioned at or near the endwalls 24. Additionally,cooling holes can be provided in the platforms 24, such as in any of thematefaces 26 and/or 28, and/or in any of the flow modifying edges 38,40, 42 and/or 44.

Any relative terms or terms of degree used herein, such as“substantially”, “essentially”, “generally” and the like, should beinterpreted in accordance with and subject to any applicable definitionsor limits expressly stated herein. In all instances, any relative termsor terms of degree used herein should be interpreted to broadlyencompass any relevant disclosed embodiments as well as such ranges orvariations as would be understood by a person of ordinary skill in theart in view of the entirety of the present disclosure, such as toencompass ordinary manufacturing tolerance variations, incidentalalignment variations, alignment or shape variations induced by thermalor rotational operational conditions, and the like.

While the invention has been described with reference to an exemplaryembodiment(s), it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof. Therefore, it is intended that the inventionnot be limited to the particular embodiment(s) disclosed, but that theinvention will include all embodiments falling within the scope of theappended claims.

DISCUSSION OF POSSIBLE EMBODIMENTS

The following are non-exclusive descriptions of possible embodiments ofthe present invention.

An airfoil for use in an airfoil cascade includes an airfoil workingportion; an endwall adjoining an end of the airfoil working portion, theendwall having a leading edge, a trailing edge, a first mateface, and asecond mateface, wherein the first and second matefaces are arrangedopposite one another, and wherein the leading edge, trailing edge, andfirst and second matefaces collectively define a perimeter of theendwall; a forward zone defined by the endwall that extends to theleading edge, wherein the first and second matefaces are each orientedat an angle α_(II) relative to a radial direction in the forward zone;an aft zone defined by the endwall that extends to the trailing edge,wherein the first and second matefaces are each oriented at an angleα_(I) relative to a radial direction in the aft zone, and wherein theangles α_(I) and α_(II) are not equal; and a middle zone defined by theendwall in between the forward and aft zones, wherein the first andsecond matefaces transition between the angle α_(II) and the angle α_(I)in the middle zone.

The airfoil of the preceding paragraph can optionally include,additionally and/or alternatively, any one or more of the followingfeatures, configurations and/or additional components:

the endwall can comprise a platform adjoining a root end of the airfoilworking portion;

the endwall can be integrally and monolithically formed with the airfoilworking portion;

the angle α_(II) can be in the range of approximately 0°≦α_(II)≦45°, andthe angle α_(I) can be in the range of approximately −45°≦α_(I)≦0°;

the angle α_(II) can be in the range of approximately −45°≦α_(II)≦0°,and the angle α_(I) can be in the range of approximately 0°−α_(I)≦45°;

the angle α_(II) can be approximately 0°, and the angle α_(I) can be inthe range of approximately 0°<α_(I)<45°;

the angle α_(II) can be in the range of approximately −45°<α_(II)<0°,and the angle α_(I) can be approximately 0°; and/or

a flowpath surface adjacent to each of the first and second matefacesand the leading and trailing edges, and that extends to the perimeter ofthe endwall; a first flow modifying edge between the first mateface andthe flowpath surface, wherein the first flow modifying edge extendsalong an entire length of the first mateface between the leading edgeand the trailing edge; and a second flow modifying edge between thesecond mateface and the flowpath surface, wherein the second flowmodifying edge extends along an entire length of the second matefacebetween the leading edge and the trailing edge.

An airfoil for using in an airfoil cascade includes an airfoil workingportion; an endwall adjoining an end of the airfoil working portion, theendwall having a leading edge, a trailing edge, a first mateface, asecond mateface, and a flowpath surface, wherein the first and secondmatefaces are arranged opposite one another, and wherein the leadingedge, trailing edge, and first and second matefaces collectively definea perimeter of the flowpath surface of the endwall; a first flowmodifying edge between the first mateface and the flowpath surface,wherein the first flow modifying edge extends along an entire length ofthe first mateface between the leading edge and the trailing edge; and asecond flow modifying edge between the second mateface and the flowpathsurface, wherein the second flow modifying edge extends along an entirelength of the second mateface between the leading edge and the trailingedge.

The airfoil of the preceding paragraph can optionally include,additionally and/or alternatively, any one or more of the followingfeatures, configurations and/or additional components:

the first flow modifying edge can comprise an arcuate flow modifyingedge;

the arcuate flow modifying edge can have a radius R in a range ofapproximately 0.127 to 6.35 mm (0.005 to 0.250 inch)

the second flow modifying edge can comprise an arcuate flow modifyingedge configured substantially identically to the first flow modifyingedge;

the first flow modifying edge can comprise a chamfered flow modifyingedge;

the chamfered flow modifying edge can be defined at an angle θ withrespect to the adjoining first mateface, and the angle θ can be in therange of approximately 45° to 75°;

a forward zone defined by the endwall that extends to the leading edge,wherein the first and second matefaces each are oriented at an angleα_(II) relative to a radial direction in the forward zone, and whereinan absolute value of the angle α_(II) is in the range of approximately0°≦|α|≦45°; an aft zone defined by the endwall that extends to thetrailing edge, wherein the first and second matefaces each are orientedat an angle α_(I) relative to a radial direction in the aft zone,wherein an absolute value of the angle α_(I) is in the range ofapproximately 0°≦|α|≦45°, and wherein the angles α_(I) and α_(II) arenot equal; and a middle zone defined by the endwall in between theforward and aft zones, wherein the first and second matefaces transitionbetween the angle α_(II) and the angle α_(I) in the middle zone; and/or

the first and second matefaces can both be substantially planar withinthe forward and aft zones.

A method includes providing an endwall adjoining an end of an airfoilworking portion, the endwall having a leading edge, a trailing edge, afirst mateface, and a second mateface, wherein the first and secondmatefaces are arranged opposite one another, and wherein the leadingedge, trailing edge, and first and second matefaces collectively definea perimeter of the endwall; defining the first and second matefaces atan angle α_(II) relative to a radial direction in a forward zone of theendwall that extends to the leading edge; defining the first and secondmatefaces at an angle α_(I) relative to the radial direction in an aftzone of the endwall that extends to the trailing edge, and wherein theangles α_(I) and α_(II) are not equal; and defining a middle zone of theendwall in between the forward and aft zones, wherein the first andsecond matefaces transition between the angle α_(I) and the angle α_(II)in the middle zone.

The method of the preceding paragraph can optionally include,additionally and/or alternatively, any one or more of the followingfeatures and/or additional steps:

defining a first flow modifying edge between the first mateface and theflowpath surface along an entire length of the first mateface betweenthe leading edge and the trailing edge, wherein the flowpath surface isadjacent to each of the first and second matefaces and the leading andtrailing edges; and defining a second flow modifying edge between thesecond mateface and the flowpath surface along an entire length of thesecond mateface between the leading edge and the trailing edge.

A method includes providing an endwall adjoining an end of an airfoilworking portion, the endwall having a leading edge, a trailing edge, afirst mateface, a second mateface, and a flowpath surface, wherein thefirst and second matefaces are arranged opposite one another, whereinthe leading edge, trailing edge, and first and second matefacescollectively define a perimeter of the endwall, and wherein the flowpathsurface is adjacent to each of the first and second matefaces and theleading and trailing edges; defining a first flow modifying edge betweenthe first mateface and the flowpath surface along an entire length ofthe first mateface between the leading edge and the trailing edge; anddefining a second flow modifying edge between the second mateface andthe flowpath surface along an entire length of the second matefacebetween the leading edge and the trailing edge.

The method of the preceding paragraph can optionally include,additionally and/or alternatively, any one or more of the followingfeatures and/or additional steps:

defining the first and second matefaces at an angle α_(II) relative to aradial direction in a forward zone of the endwall that extends to theleading edge; defining the first and second matefaces at an angle α_(I)relative to the radial direction in an aft zone of the endwall thatextends to the trailing edge, and wherein the angles α_(I) and α_(II)are not equal; and defining a middle zone of the endwall in between theforward and aft zones, wherein the first and second matefaces transitionbetween the angle α_(I) and the angle α_(II) in the middle zone;

the step of defining a first flow modifying edge can comprise definingone of forming a chamfer and forming an arcuate edge at a radius R,wherein R is in a range of approximately 0.127 to 6.35 mm (0.005 to0.250 inch); and/or

the step of defining a second flow modifying edge can comprise definingone of forming a chamfer and forming an arcuate edge at a radius R,wherein R is in a range of approximately 0.127 to 6.35 mm (0.005 to0.250 inch).

1. An airfoil for use in an airfoil cascade, the airfoil comprising: anairfoil working portion; an endwall adjoining an end of the airfoilworking portion, the endwall having a leading edge, a trailing edge, afirst mateface, and a second mateface, wherein the first and secondmatefaces are arranged opposite one another, and wherein the leadingedge, trailing edge, and first and second matefaces collectively definea perimeter of the endwall; a forward zone defined by the endwall thatextends to the leading edge, wherein the first and second matefaces areeach oriented at an angle α_(II) relative to a radial direction in theforward zone; an aft zone defined by the endwall that extends to thetrailing edge, wherein the first and second matefaces are each orientedat an angle α_(I) relative to a radial direction in the aft zone, andwherein the angles α_(I) and α_(II) are not equal; and a middle zonedefined by the endwall in between the forward and aft zones, wherein thefirst and second matefaces transition between the angle α_(II) and theangle α_(I) in the middle zone.
 2. The airfoil of claim 1, wherein theendwall comprises a platform adjoining a root end of the airfoil workingportion.
 3. The airfoil of claim 1, wherein the endwall is integrallyand monolithically formed with the airfoil working portion.
 4. Theairfoil of claim 1, wherein the angle α_(II) is in the range ofapproximately 0°≦α_(II)≦45°, and wherein the angle α_(I) is in the rangeof approximately −45°≦α_(I)≦0°.
 5. The airfoil of claim 1, wherein theangle α_(II) is in the range of approximately −45°≦α_(II)≦0°, andwherein the angle α_(I) is in the range of approximately 0°≦α_(I)≦45°.6. The airfoil of claim 1, wherein the angle α_(II) is approximately 0°,and wherein the angle α_(I) is in the range of approximately0°<α_(I)≦45°.
 7. The airfoil of claim 1, wherein the angle α_(II) is inthe range of approximately −45°≦α_(II)<0°, and wherein the angle α_(I)is approximately 0°.
 8. The airfoil of claim 1 and further comprising: aflowpath surface adjacent to each of the first and second matefaces andthe leading and trailing edges, and that extends to the perimeter of theendwall; a first flow modifying edge between the first mateface and theflowpath surface, wherein the first flow modifying edge extends along anentire length of the first mateface between the leading edge and thetrailing edge; and a second flow modifying edge between the secondmateface and the flowpath surface, wherein the second flow modifyingedge extends along an entire length of the second mateface between theleading edge and the trailing edge.
 9. An airfoil for using in anairfoil cascade, the airfoil comprising: an airfoil working portion; anendwall adjoining an end of the airfoil working portion, the endwallhaving a leading edge, a trailing edge, a first mateface, a secondmateface, and a flowpath surface, wherein the first and second matefacesare arranged opposite one another, and wherein the leading edge,trailing edge, and first and second matefaces collectively define aperimeter of the flowpath surface of the endwall; a first flow modifyingedge between the first mateface and the flowpath surface, wherein thefirst flow modifying edge extends along an entire length of the firstmateface between the leading edge and the trailing edge; and a secondflow modifying edge between the second mateface and the flowpathsurface, wherein the second flow modifying edge extends along an entirelength of the second mateface between the leading edge and the trailingedge.
 10. The airfoil of claim 9, wherein the first flow modifying edgecomprises an arcuate flow modifying edge.
 11. The airfoil of claim 10,wherein the arcuate flow modifying edge has a radius R in a range ofapproximately 0.127 to 6.35 mm (0.005 to 0.250 inch).
 12. The airfoil ofclaim 10, wherein the second flow modifying edge comprises an arcuateflow modifying edge configured substantially identically to the firstflow modifying edge.
 13. The airfoil of claim 9, wherein the first flowmodifying edge comprises a chamfered flow modifying edge.
 14. Theairfoil of claim 13, wherein the chamfered flow modifying edge isdefined at an angle θ with respect to the adjoining first mateface, andwherein the angle θ is in the range of approximately 45° to 75°.
 15. Theairfoil of claim 9 and further comprising: a forward zone defined by theendwall that extends to the leading edge, wherein the first and secondmatefaces each are oriented at an angle α_(II) relative to a radialdirection in the forward zone, and wherein an absolute value of theangle α_(II) is in the range of approximately 0°≦|α_(II)|≦45°; an aftzone defined by the endwall that extends to the trailing edge, whereinthe first and second matefaces each are oriented at an angle α_(I)relative to a radial direction in the aft zone, wherein an absolutevalue of the angle α_(I) is in the range of approximately0°≦|α_(I)|≦45°, and wherein the angles α_(I) and α_(II) are not equal;and a middle zone defined by the endwall in between the forward and aftzones, wherein the first and second matefaces transition between theangle α_(II) and the angle α_(I) in the middle zone.
 16. The airfoil ofclaim 15, wherein the first and second matefaces are both substantiallyplanar within the forward and aft zones.
 17. A method comprising:providing an endwall adjoining an end of an airfoil working portion, theendwall having a leading edge, a trailing edge, a first mateface, asecond mateface, and a flowpath surface, wherein the first and secondmatefaces are arranged opposite one another, wherein the leading edge,trailing edge, and first and second matefaces collectively define aperimeter of the endwall, and wherein the flowpath surface is adjacentto each of the first and second matefaces and the leading and trailingedges; defining a first flow modifying edge between the first matefaceand the flowpath surface along an entire length of the first matefacebetween the leading edge and the trailing edge; and defining a secondflow modifying edge between the second mateface and the flowpath surfacealong an entire length of the second mateface between the leading edgeand the trailing edge.
 18. The method of claim 17 and furthercomprising: defining the first and second matefaces at an angle α_(II)relative to a radial direction in a forward zone of the endwall thatextends to the leading edge; defining the first and second matefaces atan angle α_(I) relative to the radial direction in an aft zone of theendwall that extends to the trailing edge, and wherein the angles α_(I)and α_(II) are not equal; and defining a middle zone of the endwall inbetween the forward and aft zones, wherein the first and secondmatefaces transition between the angle α_(I) and the angle α_(II) in themiddle zone.
 19. The method of claim 17, wherein the step of defining afirst flow modifying edge comprises defining one of forming a chamferand forming an arcuate edge at a radius R, wherein R is in a range ofapproximately 0.127 to 6.35 mm (0.005 to 0.250 inch).
 20. The method ofclaim 17, wherein the step of defining a second flow modifying edgecomprises defining one of forming a chamfer and forming an arcuate edgeat a radius R, wherein R is in a range of approximately 0.127 to 6.35 mm(0.005 to 0.250 inch)